Study on Discontinuous Deformation Analysis and Modern Crustal Movement

This paper discusses the application of discontinuous deformation analysis (DDA),a powerful numerical method,to the simulation of crustal movement problems.The problems of crustal movement contain the movement of large plates to small active faults.Usually,finite element (FE) method is used to the simulation of crustal movement problems,but discontinuous faults exist in plates and discontinuous medium exist in rocks.So traditional numerical methods (especial for finite element method) are not efficient to simulate crustal movement.DDA method is better than FE method. This paper introduces the principle of DDA method.After DDA method compared with FE method,the advantage and limitation of DDA method discussed. For efficiently using DDA method in the simulation of crustal movement,the idea of developing DDA method in 2D plane coordinate system to a new DDA method in 2D spherical coordinate system is shown for the first time. 1) Establishing the function equation between displacement and its invariant of any point of the blocks on the spherical surface.Based on the basic relation formula of displacement and strain on the spherical coordinate system,the function equation of displacement (u,v) and its invariant (u₀,v₀,r₀,ε_ф,ε_θ,γ_фθ) on the spherical surface can be set up.The linear approximately expression of deformation of blocks will be assumed. 2) Establishing the relation equation of the blocks on spherical surface depending on the theory of Least Potential Energy.The potential energy expression will be separately resolved,including the stiffness stress,initial stress,points loading,volume force,inertial stress,fixed displacement of points etc.By differencing the equation,the coefficient child matrix can be got,and then added to the relation equation. 3) Establishing the kinematics equation of block system formed by a lot of blocks on the spherical surface.A mathematic expression must be achieved to describe the relation between the nearby blocks.The invasion is not allowed among the blocks.The problem of no invasion can be well resolved in high precise through adding rigidity spring on the edge of blocks.The appending of rigidity spring is judged by distance of invasion on the edge of the nearby blocks.The calculation of distance invasion will be very complex on spherical coordinate system.In order to make the calculation simple and highly efficient,local plane projection coordinate system is chose and the problem of spherical surface becomes as easy as the situation of plane coordinate. In the fourth part of the paper,focusing on researching region of geosciences,three kinds of problem of crustal movement are mentioned,and a working plan is shown.DDA method can play an important part in the areas.